In a TEM a sample, such as a thin slice of biological material or a thin slice of semiconductor material, with a thickness of typically between 2 nm to 1 μm, is irradiated with an energetic beam of electrons. The energy of the electrons is, for example, adjustable between 50 to 400 keV, although TEMs using a higher and/or lower energy are known to be used. The sample is placed in or near the objective lens of the TEM, so that the objective lens forms a first image of the sample with a magnification of, for example, 20 times.
As known to the skilled artisan a TEM has two major modes of operation, one in which the sample is imaged on the detector system, and one in which the back focal plane of the objective lens is imaged on the detector system. The back focal plane contains the diffraction pattern of the sample. The detector system can, for example, be a fluorescent screen, or a CMOS detector. The sample may be imaged on the detector with a magnification of, for example, 106 times, with a corresponding resolution of 100 pm or less.
A typical TEM is equipped with two stigmators after the objective lens, one in a plane close to the objective lens for correcting the astigmatism in imaging mode (when the sample is imaged), and one close to the plane of the first intermediate imaging for correcting the astigmatism in diffraction mode (when the diffraction pattern is imaged).
In imaging mode the sample is imaged on, for example, the fluorescent screen of the TEM, or another detector such as a CCD camera, a CMOS camera, or the like. The objective stigmator is used to correct the astigmatism of the objective lens, and tuning is done by observing the image of the sample.
In diffraction mode the diffraction plane is imaged on, for example, the fluorescent screen of the TEM, or another detector such as a CCD camera, a CMOS camera, or the like. The diffraction stigmator is used to correct the astigmatism of the diffraction lens, and tuning is done by observing the image of the diffraction pattern.
A problem using one stigmator for correcting the astigmatism is that Linear Distortion (LD) arises: the magnification in two perpendicular directions may be different. This is shown in FIG. 1. FIG. 1A schematically shows a beam with astigmatism, where the strength of the objective lens in one direction is slightly different from its strength in another direction. This can be caused by, for example, imperfections in the shape of the objective lens. We choose x and y axes such that the x-z plane is the plane in which the objective lens is weakest, and the y-z plane is the plane in which the objective is the strongest. The focus in the x-z plane is slightly different from the focus in the y-z plane. In FIG. 1B this is corrected with a stigmator, and the foci in the x-z and the y-z plane coincide. However, the angles βx and βy are not identical, and, as the angular magnification in the x-z plane differs from the angular magnification of the y-z plane, also the spatial magnification differs between the x-z plane and the y-z plane.
It is noted that, as the stigmator has different effects in the x-z and the y-z plane, the magnification error introduced by using only one stigmator is linear distortion (LD): the magnification in the x- and the y-direction differ. FIG. 1C shows a solution to this problem by using a second stigmator.
The use of two stigmators to correct LD in diffraction mode is known from “A Method to Correct Elliptical Distortion of Diffraction Patterns in TEM”, Hou et al., Microsc Microanal 14 (suppl. 2) 2008, page 1126. In said article the magnification error is dubbed elliptical error. To determine this error the objective lens stigmator of a TEM is set on an arbitrarily value, the diffraction lens stigmator is adjusted accordingly to minimize the astigmatism in the diffraction image, and the LD (here named elliptical distortion) in the diffraction pattern is measured. This is repeated for different values of the objective lens stigmator to form a 2D contour plot representing the LD for all objective lens stigmator settings (and correspondingly optimized diffraction lens stigmator settings).
The use of two stigmators to correct LD in a lithographic apparatus while imaging a reticle on a wafer is known from U.S. Pat. No. 6,388,261. The patent describes an apparatus in which the reticle is imaged by a doublet of lenses, whereby the magnification can be tuned. Each of the two lenses is surrounded by a stigmator, in which one stigmator is used mainly to correct the astigmatism of the doublet and the other one to correct mainly the LD.
The above two examples show that it is in principle possible and known to adjust astigmatism and LD simultaneously with two stigmators.
As known to the skilled artisan the position of a stigmator cannot be arbitrarily chosen: the strength of the magnetic or electrostatic field used in a stigmator scales linearly with the distance to the axis. Therefore stigmating a beam with a small diameter requires a larger excitation of a stigmator than stigmating a beam with a large diameter. For a beam diverging from or to an intermediate image, the beam diameter scales linearly with the distance from the intermediate image. Thus at the image, where the beam has a cross-over, a stigmator even has no stigmating effect. Furthermore, the effect of a stigmator also scales linearly with the distance between the stigmator and the plane where the image is formed. Thus for a beam diverging from or to an intermediate image, the effect of a stigmator thus scales quadratically with the distance of the stigmator to the plane where the image is formed.
Therefore, a stigmator is preferably placed at the position where the beam has a large diameter and far from the plane where the image is formed.
As a TEM has two modes of operation, one in which the image plane is imaged and one in which the diffraction plane is imaged, a typical TEM is equipped with two stigmators between the sample and the imaging system, one in a plane close to the objective for correcting the astigmatism in the image when the image is imaged, and one near the diffraction lens (that is: the first lens of the imaging system after the objective lens) for correcting the astigmatism in the diffraction plane when the diffraction plane is imaged.
The resulting two degrees of freedom (one for each stigmator) are used to correct astigmatism in the objective and diffraction plane.
The two stigmators can work together to form a virtual plane in which the combined action occurs. This combined action can be the correction of astigmatism and the correction of the LD. This plane can be chosen to coincide with the plane where the object resides, or to coincide with the diffraction plane.
A problem arises when using two stigmators to correct astigmatism in the two modes (imaging mode and diffraction mode) and also correct for LD with those stigmators: when switching between modes, also the excitation of the stigmators must be changed. This is explained as follows: in the imaging mode the imaging stigmator is used to correct the astigmatism and the other stigmator, the diffractor stigmator, to correct the LD. In diffraction mode, the diffractor stigmator is used to correct for astigmatism and the other stigmator, the objective stigmator, to correct the LD. The change in excitation causes a different ohmic heat production in the coils of the stigmator, typically a change of several watt, resulting in drift of the image due to the resultant temperature drift. The required stabilization time in the order of tens of minutes. Also hysteresis may occur, especially when iron yokes are used.
Accordingly, there is a need to provide an apparatus and method for correcting astigmatism in two planes, and correct Linear Distortion simultaneously, without drift caused by different excitation of the stigmators.